evidence for active control of rectus extraocular muscle...

Evidence for Active Control of Rectus ExtraocularMuscle Pulleys

Joseph L. Demer,1,2 Sei Yeul Oh,1,3 and Vadims Poukens1

PURPOSE. Connective tissue structures constrain paths of the rectus extraocular muscles (EOMs),acting as pulleys and serving as functional EOM origins. This study was conducted to investigate therelationship of orbital and global EOM layers to pulleys and kinematic implications of this anatomy.

METHODS. High-resolution magnetic resonance imaging (MRI) was used to define the anterior pathsof rectus EOMs, as influenced by gaze direction in living subjects. Pulley tissues were examined atcadaveric dissections and surgical exposures. Human and monkey orbits were step and seriallysectioned for histologic staining to distinguish EOM fiber layers in relationship to pulleys.

RESULTS. MRI consistently demonstrated gaze-related shifts in the anteroposterior locations ofhuman EOM path inflections, as well as shifts in components of the pulleys themselves. Histologicstudies of human and monkey orbits confirmed gross examinations and surgical exposures toindicate that the orbital layer of each rectus EOM inserts on its corresponding pulley, rather thanon the globe. Only the global layer of the EOM inserts on the sclera. This dual insertion wasvisualized in vivo by MRI in human horizontal rectus EOMs.

CONCLUSIONS. The authors propose the active-pulley hypothesis: By dual insertions the global layerof each rectus EOM rotates the globe while the orbital layer inserts on its pulley to position itlinearly and thus influence the EOM’s rotational axis. Pulley locations may also be altered inconvergence. This overall arrangement is parsimoniously suited to account for numerous aspectsof ocular dynamics and kinematics, including Listing’s law. (Invest Ophthalmol Vis Sci. 2000;41:1280–1290)

Initial attempts to mathematically model binocular align-ment showed the importance to extraocular muscle (EOM)action of EOM paths and the pivotal mechanical role of

orbital connective tissues. The need for EOM path data moti-vated early radiographic studies in monkeys1 and humans,2

suggesting that paths of rectus EOMs are stabilized relative tothe orbit. A decade ago, Miller3 used relatively low-resolutionMRI with three-dimensional (3-D) reconstruction to demon-strate stability of rectus EOM belly paths throughout the ocu-lomotor range.3 The further demonstration by MRI that EOMpaths are little affected by large surgical transpositions of theirtendons provided strong evidence for EOM path constraint bypulleys coupled to the orbit.4,5

Recent anatomic studies of whole orbits confirmed thateach rectus EOM passes through a pulley consisting of anencircling ring or sleeve of collagen, located near the globe

equator in Tenon’s fascia.6,7 The microscopic structure ofpulleys is stereotypic.6–9 Pulley collagen fibrils are dense andorganized in an interdigitating configuration suited to highinternal rigidity.10 Pulleys are coupled to the orbital wall,adjacent EOMs, and equatorial Tenon’s fascia by bands con-taining collagen, elastin, and smooth muscle (SM). Abundantelastic fibers in and around pulleys6,7 provide reversible exten-sibility essential to these resilient tissues.11 Suspensory bandsof the pulleys contain SM6,7 with rich autonomic innervation.7

Pulleys have important implications for EOM action be-cause the functional origin of an EOM is at its pulley.12 It is thusnot surprising that coronal plane locations of rectus pulleys,inferred from EOM paths in living subjects, are not only ste-reotypic in primary gaze, but are also stable in secondary gazepositions.13 Evidence of the mechanical importance of pulleysis the finding that their heterotopy in the coronal plane isassociated with predictable patterns of incomitant strabis-mus.14 Theoretical studies of ocular kinematics suggest thatsuitable anteroposterior location of pulleys could implement alinear oculomotor plant, one that appears commutative to thebrain.15 Lower resolution MRI of rectus paths after surgicaltransposition of EOM insertions suggests that the anteroposte-rior location of pulleys is consistent with the foregoing theo-retical requirements,5 a finding now confirmed by higher res-olution MRI of normal rectus EOM path inflections insecondary gaze positions (Clark and Demer, unpublished data,2000).

Recent advances in orbital imaging technique have im-proved earlier orbital MRI resolution by an order of magnitude.Surprisingly, technical limitations in existing orbital anatomicdata now make them inadequate for comparison to the increas-

From the 1Department of Ophthalmology, Jules Stein Eye Insti-tute, and the 2Department of Neurology, University of California, LosAngeles; and the 3Department of Ophthalmology, Samsung MedicalCenter, Sungkyunkwan University School of Medicine, Seoul, Korea.

Presented in part at the Wenner–Gren International Symposiumon Advances in Strabismus Research: Basic and Clinical Aspects, June25, 1999, Stockholm, Sweden.

Supported by US Public Health Service, National Eye InstituteGrant EY-08313 and Core Grant EY-00331. JLD received a Research toPrevent Blindness Lew R. Wasserman merit award and is the Larraineand David Gerber Professor of Ophthalmology.

Submitted for publication September 14, 1999; revised December9, 1999; accepted December 20, 1999.

Commercial relationships policy: N.Corresponding author: Joseph L. Demer, Jules Stein Eye Institute,

100 Stein Plaza, UCLA, Los Angeles, CA 90095-7002. [email protected].

Investigative Ophthalmology & Visual Science, May 2000, Vol. 41, No. 61280 Copyright © Association for Research in Vision and Ophthalmology

ing quality of modern MRI of living EOMs. A major limitationhas resulted from exenteration of orbital tissues before histo-logic processing. Release of connective tissue tension in anonphysiologic manner by dissection of individual EOMs fromunfixed orbits can distort anatomic relationships. An improvedtechnique involves en bloc exenteration of the orbital softtissues from their bony supports, followed by fixation.6,7 Thismethod maintains most orbital topology, but not necessarilynormal distances. Even so, dissection of the anterior periorbitafrom the orbital rim damaged the pulley supports. These arti-facts limited interpretation of prior anatomic studies of theorbital connective tissues.

It has long been recognized that rectus EOMs of mammalscontain two distinct layers.16–20 The global layer containsthree types of singly innervated fibers (SIFs) and one type ofmultiply innervated fiber (MIF); the orbital layer contains onetype of SIF and one type of MIF. Classic studies have demon-strated that although the global layer is continuous from theannulus of Zinn to the tendinous insertion on the globe, theorbital layer terminates posterior to the scleral insertion.16,21

Because these studies were performed before appreciation ofthe existence of pulleys, it is unclear from the literature howthe EOM orbital layer may relate to contemporary understand-ing of pulley anatomy and function.

Technical improvements have made it possible to recon-struct detailed orbital histology without removal from the sup-porting bones, thus maintaining normal spatial relationships.The present study was thus designed to exploit improvementsin MRI in living subjects, as well as histology in cadavers, forstudy of the precise relationship between EOM layers and thecorresponding pulleys. These data were examined in the con-text of surgical exposures of living tissues and were interpretedin the context of contemporary concepts of the contribution ofpulleys to binocular kinematics.

METHODS

Magnetic Resonance Imaging

High-resolution MR images were collected from volunteerswho gave written, informed consent to a protocol conformingto the Declaration of Helsinki and approved by the HumanSubject Protection Committee at the University of California,Los Angeles. Imaging was performed using a 1.5-T scanner(Signa; General Electric, Milwaukee, WI). Crucial aspects ofthis technique, described in detail elsewhere, include use of adual-phased surface coil array (Medical Advances, Milwaukee,WI) to improve signal-to-noise ratio and fixation targets toavoid motion artifacts.22 Images of 2-mm thickness in a matrixof 256 3 256 were obtained over a field of view of 8 cm for aresolution in plane of 312 mm. Axial images were obtained, aswell as quasicoronal images perpendicular to the long axis ofthe orbit.

Tissue Preparation

Five human orbits (aged 44–93 years) were exenterated enbloc at autopsy through an intracranial approach within 24hours of death. These were fixed for at least five days in 10%neutral buffered formalin with the periorbita intact but sepa-rated from bony support. Three additional human orbits (aged17 months to 57 years) were obtained from a tissue bank(IIAM, Scranton, PA), in heads fresh frozen shortly after death.

The frozen heads were slowly thawed in 10% neutral bufferedformalin. Three monkeys, a rhesus (Macaca mulatta), a fas-cicularis (Macaca fascicularis), and a cebus (Cebus apella),were killed in conformity with recommendations of the Amer-ican Veterinary Medical Association and ARVO Statement forthe Use of Animals in Ophthalmic and Vision Research andperfused with fixative through the aorta. The intact, fixed rightorbits of the three humans and three monkeys were thenremoved in continuity with the eyelids and orbital bones, thelatter being carefully thinned under magnification by using ahigh speed-drill. These fixed right orbits were then decalcifiedfor 24 hours at room temperature in 0.003 M EDTA and 1.35 NHCl. The left orbit of the cebus monkey was exenterated afterfixation, and longitudinal dissections were made to removeeach rectus EOM in continuity with its adjacent pulley andunderlying sclera.

At autopsy of an adult male human conducted within 8hours of death, all EOMs were harvested in continuity withtheir contiguous connective tissues. After atraumatic enucle-ation of the globes using surgical technique and magnification,EOMs were isolated and excised, with orientation carefullymaintained. Representative EOMs and their contiguous pulleyswere pinned to cardboard at anatomic length and orientationbefore fixation in 10% neutral buffered formalin.

Formalin-fixed tissues were dehydrated in graded solu-tions of alcohol and chloroform, embedded in paraffin, andserially sectioned at 10-mm thickness, as previously de-scribed.6,7 Whole orbits were serially sectioned in the coronalplane. Individual human EOMs, as well as EOMs in continuitywith the sclera in the cebus monkey, were step sectionedlongitudinally in the vicinity of pulleys at intervals of 200 mm,and transversely at intervals of 200 mm posterior to them. Allsections were mounted on gelatin-coated glass slides.

Masson’s trichrome stain was used to show muscle andcollagen and van Gieson’s stain to show elastin.23 As previouslydescribed,7 SM was confirmed using monoclonal mouse anti-body to human SM a-actin (Dako, Copenhagen, Denmark)applied at 4°C overnight at dilutions of 1:100 to 1:500. Theantigen–antibody reaction for human SM a-actin was visualizedusing the ABC kit with blue chromogen (Alkaline PhosphataseKit 3; Vector, Burlingame, CA).24

Orbital dissections were performed in three fresh adulthuman cadavers to isolate the medial rectus (MR) pulley. Se-lected tissues were excised and processed histologically toconfirm their composition. Findings at these dissections werecorrelated with findings at routine strabismus surgeries per-formed by an author (JLD) in which rectus EOMs were ex-posed and clinical photographs taken.

RESULTS

MRI was performed in right and left gaze in six adult volunteersin axial image planes aligned with the horizontal rectus EOMsto visualize the fine structure of the insertions. Each horizontalEOM was typically represented in five adjacent image planes.Favorable image planes, ones typically including the superioror inferior regions of the horizontal rectus EOMs rather than inthe central portion, consistently demonstrated the presence ofone or more dark bands running anteriorly and peripherallytoward the orbital rim. The dark bands were typically betterdemonstrated in different image planes for the MR and lateral

IOVS, May 2000, Vol. 41, No. 6 Active Control of Extraocular Muscle Pulleys 1281

rectus (LR) muscles. Histologic evidence indicates that thisdark band represents the connective tissue suspension of thecorresponding EOM pulley and that the orbital layer of theEOM inserts onto the connective tissue of the dark band.

The insertion of the MR orbital layer into its pulley isillustrated for four representative subjects of various ages inFigure 1A. In dextroversion, the MR path for the abductingright eye is inflected at roughly the point at which the dark

band joins the EOM belly. This inflection, more obvious inimage planes including the central part of the MR, correspondsto the MR pulley. The insertion of the dark band on the MR’sorbital surface was more anterior in abduction than in adduc-tion (Fig. 1A). More central image planes (for example, Fig. 1B)demonstrated a corresponding posterior shift in the MR inflec-tion point with adduction. The dark band was more prominentin older subjects (Fig. 1A). These findings, supported by histo-

FIGURE 1. Axial MRI demon-strating dual insertions of horizon-tal rectus muscles in 2-mm-thickimage planes at resolution of 312mm. In each case, the right side ofthe subject is represented on theleft side of the image. (A) Orbitallayer insertion of MR muscles offour representative subjects ofvarious ages fixating a target indextroversion. Insertion of the or-bital layer into the pulley (ar-rows) occurred roughly at the MRpath inflection point and was gen-erally farther posterior for the ad-ducting left eye than for the ab-ducting right eye. The dual natureof the MR insertion was more ob-vious in the older than in theyounger subjects. A prosthetic in-traocular lens is visible in the sub-ject on the lower right. Imageswere intentionally decentered tofavor the right orbit to improveresolution. (B) Orbital layer inser-tion of LR muscles on the corre-sponding pulleys of a representa-tive subject in levoversion anddextroversion. Thick arrows de-note insertion of the orbital layeron a dark gray band at the LRpath inflection point produced bythe LR pulley. Note the more pos-terior location of the LR orbitallayer insertion in abduction thanin adduction. The MR orbital layerinsertion on the MR pulley is alsovisible (thin arrows).

1282 Demer et al. IOVS, May 2000, Vol. 41, No. 6

logic evidence below, indicate that the insertion of the MRorbital layer is on the MR pulley that in turn inflects the MR’spath and that the pulley moves posteriorly from abduction toadduction.

A similar dark band was demonstrable for the LR muscle,originating at the path inflection produced by the LR pulleyand extending anteriorly and laterally toward the orbital rim.Figure 1B demonstrates both prominent inflections producedby the horizontal rectus pulleys and the presence of dark bandsat the inflections in dextro- and levoversion. The junction ofthe dark band with the LR moved posteriorly from abductionto adduction. Again, the junction of the dark band with the LRcorresponds to the insertion of the LR orbital layer on itspulley.

Insertion of the orbital layer of horizontal rectus EOMsinto the connective tissues of the peripheral orbit was alsoconsistently appreciated in coronal plane imaging performedin eight subjects. The orbital layer insertion of the MR musclecould be visualized in nearly every orbit as one or more darkbands isodense with EOM extending radially toward the medialorbital wall (Fig. 2). The MR orbital layer insertion in Figure 2typifies the most common pattern of three prominent bands.The anteroposterior extent of the orbital layer insertion was

focal, so that it was imaged in only one or two adjacent2-mm-thick coronal planes. As seen in Figure 2, large horizontalgaze shifts caused a corresponding shift in the anteroposteriorlocation of the MR orbital layer insertion. In 28° adduction, theMR orbital layer insertion was relatively posterior at the level ofthe globe–optic nerve junction. In primary gaze, the MR orbitallayer insertion moved two image planes (4 mm) and anothertwo image planes (4 mm) anteriorly in 28° abduction for a totaltravel of approximately 8 mm.

Cadaveric and surgical dissections were begun sharply atthe limbus and completed using only gentle blunt techniqueparallel to the rectus tendons. Each tendon was engaged at theinsertion using a muscle hook, with which tension was appliedto rotate the eye away from the EOM. The conjunctiva andadjacent connective tissues were retracted toward the orbitalperiphery. Cadaveric findings were consistent with intrasurgi-cal findings using similar exposure. Figure 3 shows a surgicalexposure of the MR, and illustrates multiple dense, whitefibrous bands extending from the orbital surface of the MRmuscle and inserting into the glistening white tissue on itsnasal side. This adjacent connective tissue was confirmed incadaveric material to form the pulley ring encircling the MR.During maximal abduction, the insertion of the MR orbital

FIGURE 2. Sets of contiguous 2-mm-thick quasicoronal MRI images of a representative right orbit in 28° adduction, straight-ahead gaze, and abduction.Images are ordered from posterior at left to anterior at right, with identical head positioning for all gaze positions. The thick white arrow in each rowdemonstrates orbital layer insertion of the MR muscle on its pulley. The image planes including the insertion are enlarged in the bottom row for eachgaze position. The insertion of the orbital layer is seen as three dark bands running radially toward the medial orbit. The orbital layer insertion wasposterior in adduction and moved two image planes (4 mm) anteriorly in straight-ahead gaze and another two image planes (4 mm) anteriorly inabduction. IR, inferior rectus muscle; LLA, lateral levator aponeurosis; LR, lateral rectus muscle; MR, medial rectus muscle; SO, superior oblique muscle;SR, superior rectus muscle.


layer into its pulley was approximately 12 mm posterior to theinsertion of the MR global layer on the sclera. This distancedepends on horizontal eye position. Findings were similar forthe other rectus EOMs.

Histochemistry and Immunohistochemistry

In low-power micrographs of the mid to posterior orbit wherethe orbital layer was present, Masson’s trichrome stain clearlydistinguished the global from the orbital layers of each rectusEOM on the basis of larger and redder fibers in the former, andthe smaller, more purple fibers in the latter (Fig. 4). Thedistinction was clearer at higher power (Fig. 5). The orbitallayer, where present, was always on the orbital surface of anyEOM but typically encompassed most of the periphery of theEOM in a C-shape to include some of the global surface aswell.16 All fibers of the levator palpebrae superioris (LPS)resembled rectus global layer fibers. In the LPS an orbital layerwas entirely absent. Serial sections were examined to locatethe rectus pulleys, consisting of rings of dense collagen encir-cling the rectus EOMs. In every rectus EOM examined inhumans and monkeys, fibers of the orbital layer inserted byshort tendons in their respective pulleys and did not continueanteriorly to them. Thus, only the global layer of each EOM wascontinuous with the long insertional tendon on the globe. Theorbital layer insertion of the LR on its pulley through shortcollagenous tendons is illustrated in Figure 5.

Van Gieson’s elastin stain demonstrated dense elastin inthe insertions of rectus orbital layers on their pulleys. Figures6A and 6B are adjacent coronal sections at lower power dem-onstrating collagen (blue in Fig. 6A) and elastin (black in Fig.6B) in a human MR pulley ring, at the point of orbital layerinsertion. Higher power views of the lower right part of theimage (black rectangle) demonstrate a bundle of orbital layerfibers completely surrounded by pulley collagen (Fig. 6C) stiff-

ened by fine, black elastin fibers inserting directly on themuscle bundle itself (Fig. 6D).

In all orbits studied there was a prominent crescent of SMnear the globe equator extending from the nasal border of thesuperior rectus (SR) pulley nasal to the MR pulley and termi-nating on the nasal border of the inferior rectus (IR) pulley. Forconsistency with Muller25 (cited by Page26) this prominentdeposit of SM will be referred to as the peribulbar muscle.

FIGURE 3. Surgical exposure of insertion of MR muscle on its pulley.A hook has been placed beneath the scleral insertion of the MR andtraction applied to abduct the globe. The glistening white tissue at theaspect nasal of the MR (under tension from a retractor) forms theanterior part of the pulley and is joined to the orbital surface of the MRby fibrous bands located approximately 12 mm posterior to the scleralinsertion of the MR with the eye maximally abducted. The cornea ispartially covered by a pledget.

FIGURE 4. Low-power coronal photomicrograph of 17-month-old hu-man right orbit stained with Masson’s trichrome to distinguish orbital(more purple on surface) and global muscle (more red in EOM coreand on global surface) fiber layers in the mid and posterior orbit. LPSdoes not have an orbital layer. Abbreviations as in Figure 2.

FIGURE 5. Higher power coronal photomicrograph of the LR of a17-month-old human stained with Masson’s trichrome demonstratinginsertion of the orbital layer on fine, collagenous tendons (arrow-heads) contiguous with the dense collagen (blue) of the LR pulley.Global layer fibers are brighter red than orbital layer fibers and aredemarcated by the broken green line. IO, inferior oblique muscle.


The insertion of rectus orbital layer fibers on their respec-tive pulleys was also confirmed by longitudinal sectioning ofrectus EOMs in the cebus monkey orbit and in one humanorbit. This is shown for a human LR in Fig. 7. The lower powerview in Fig. 7A confirms that the orbital layer does not extendanteriorly to the LR pulley. The higher power view of the sameregion shown in Fig. 7B confirms that the orbital layer insertionis through particularly dense, short collagenous tendons thatappear as focally dark blue terminations of orbital layer fibers.

DISCUSSION

Fundamental Anatomic Insight

Based on the number of abducens motor neurons, the averagenumber of muscle fibers innervated by each neuron, and theaverage tension produced by each fiber, Goldberg et al.27,28

estimated that the LR muscle should deliver approximatelytwice the force actually measured at its tendinous insertion onthe globe during tetanic stimulation. The present study maypartly explain the enigmatic question of what happened to theother half of the EOM force.27 The MRI, gross anatomic, andhistologic observations here support functional specializationof the two laminae of rectus EOMs. The global layer inserts onthe sclera as classically recognized, but the orbital layer, con-sistent with its classic termination before the scleral inser-tion,16,21,29 inserts instead on the corresponding pulley. Wedemonstrate elsewhere that the two EOM laminae containroughly equal numbers of fibers.30 The orbital layers are ideallyplaced to control the anteroposterior positions of the pulleys,moving them posteriorly during contraction as seen on axialMRI from the positions of the EOM path inflections (Fig. 1).

FIGURE 6. Adjacent 10-mm coronalsections of 17-month-old human MRstained with Masson’s trichrome (A,C) and van Gieson’s elastin stain (B,D) demonstrating insertion of the or-bital layer on the encircling ring ofthe MR pulley. Fine rectangles at thelower right of (A) and (C) are mag-nified in (B) and (D) to demonstratean orbital layer muscle fiber bundlecompletely encircled by dense colla-gen (blue) and penetrated by elastinfibrils (black) of the pulley.

FIGURE 7. Longitudinal section of LR of a 57-year-old human stainedwith Masson’s trichrome demonstrating insertion of the orbital layerinto collagen of the pulley. (A) Low power. Arrows denote insertion oforbital layer fibers into blue pulley collagen. Junction between thepurple orbital and red global layers delineated by a green dotted line.(B) Higher power. Note extensive interdigitation of pulley collagenwith terminating orbital layer fibers.


Corresponding anteroposterior motion of connective tissuecomponents of the MR pulley with horizontal gaze are alsodemonstrable by axial (Fig. 1) and coronal (Fig. 2) MRI. Theorbital layer of a rectus EOM probably exerts force on thesclera only indirectly, through changes in the path length ofthe global layer as determined by the location of the pulley.Contraction of the global layer of a rectus EOM mainly exertsforce on the globe through the classic insertion and second-arily tends to stretch the fibromuscular pulley suspensions6,7

that deflect the rectus EOM path away from a shorter straight-line path. Notwithstanding this indirect effect, it seems likelythat most of the force of the global layer acts to rotate theglobe, and most of the force of the orbital layer acts to positionthe corresponding pulley linearly. This emerging concept ofthe anatomy of the EOMs is diagrammed in Figure 8, and weterm it the active-pulley hypothesis.

Implications for Ocular Kinematics

The pulleys are constituted to regulate ocular kinematics, therotational properties of the eye. Rotations of any 3-D object arenot mathematically commutative; that is, final eye orientationdepends on the order of rotations.31 Angular velocity of a 3-Dobject is not equal to the rate of change of its orientation butrather is a complex function related to both the time derivativeand to instantaneous eye orientation.32,33 Each combination ofhorizontal and vertical eye positions could, for an arbitrary 3-Dobject, be associated with infinitely many torsional positions.34

The eye is fortunately constrained in its torsional freedom(with the head upright and immobile) by a relationship knownas Donders’ law, stating that there is only one torsional eye

position for each combination of horizontal and vertical eyepositions.32 Listing’s law, a specific case of the more generalDonders’ law, states that any physiologic eye orientation canbe reached from any other by rotation around a single axis, andthat all such possible axes lie in a single plane, Listing’s plane.Listing’s law is satisfied if for any eye movement the axis ofocular rotation shifts by exactly one half of the shift in ocularorientation.33 This is the so-called Listing’s half-angle rule.

Before pulleys were known, Listing’s law was presumedto be implemented entirely by complex neural commands tothe EOMs. However, experiments have not identified a neuralsubstrate for Listing’s law. In the superior colliculus, saccadesare encoded as the two-dimensional (horizontal and vertical)rate of change of eye orientation, implying that any computa-tion of the third dimension, torsion, is accomplished down-stream.15,35 Even in the oculomotor nucleus and rostral inter-stitial nucleus of the medial longitudinal fasciculus, saccadicburst commands are better correlated with rate of change of3-D eye position than with angular eye velocity.35,36 Neverthe-less, Listing’s law is presumed to have a neural basis35 becauseit is systematically violated by the vestibulo-ocular reflex(VOR)37 and during sleep.38 The VOR is a phylogeneticallyancient reflex that stabilizes images of fixed objects on theretina during head motion. An ideal VOR would have an axis ofocular rotation exactly matching that of the head, rather thanshifting by half the change in eye orientation. Empirically, theaxis of the VOR shifts by one fourth of the shift of eye orien-tation, so that the VOR follows a quarter-angle rule.37

The pulleys form a natural mechanical substrate for List-ing’s law and several other previously mysterious aspects ofocular kinematics.15 Figure 9 is a side view of a diagrammaticglobe showing a horizontal rectus EOM in the top panel. Therotational axis of the rectus EOM is perpendicular to the lineconnecting its pulley with the scleral insertion. Thus the rota-tional axis of the horizontal rectus EOM is vertical in straight-ahead gaze. Now consider the situation during visual fixationof a horizontally centered target at an angular elevation of anglea. If the distance from the pulley to the globe center D1 isequal to the distance from the insertion to the globe center D2,then the rotational axis tilts posteriorly by angle a/2, preciselythe requirement of Listing’s law. A recent study of EOM pathinflections in secondary gaze positions such as this examplehas demonstrated that in straight-ahead gaze the four rectuspulleys are indeed located in the positions required by thehalf-angle rule (Clark and Demer, unpublished data, 2000).

For a physiologic VOR, an orbit obeying the half-angle rulewould require a neural controller performing a complicatedtensor multiplicative comparison between eye orientation andangular velocity, and would have to do so using both sensoryand motor coordinate system transformations.39 A simpler ex-planation involves a posterior shift in pulley positions duringthe VOR (Fig. 9, lower). Selective orbital layer contractioncould displace the pulley posteriorly so that D1 5 3D2. Thiswould shift the rotational axis of the EOM by approximatelyone fourth the change in eye orientation, implementing thequarter-angle rule. Separate motor neuron pools, or differingsynaptic input weighting in the same motor neuron pool,could implement larger relative pulley motion during the VORthan during other types of eye movement. Motor neuronsprojecting to the orbital layer may be expected to have highergain during the VOR than neurons projecting to the globallayer. This idea is consistent with observations that motor unit

FIGURE 8. Structure of orbital connective tissues and their relation-ship to the fiber layers of the rectus muscles. Coronal views repre-sented at levels indicated by arrows in horizontal section. PM, peri-bulbar smooth muscle. Remaining abbreviations as in Figure 2.


behavior may be specialized for particular types of eye move-ments.40

In tertiary (oblique) gaze positions, pulley behavior canstill explain Listing’s law as illustrated in Figure 10, a top viewof a schematic orbit showing the MR and LR muscles. Begin-ning in primary position in the upper panel, the secondarypositions of elevation and depression can be attained in con-formity to Listing’s half-angle rule as explained earlier, if thedistance from the pulley to the globe center D1 is equal to thedistance from the insertion to the globe center D2. Beginningin adduction as diagrammed in the lower panel, the tertiary

positions of adducted elevation and adducted depression canbe attained in conformity to Listing’s law once again if thedistance from the pulley to the globe center D1 is equal to thedistance from the insertion to the globe center D2. DistancesD1 and D2 are referenced to the globe, not to the orbit. Toimplement Listing’s law, shifts in the anteroposterior positionof the pulleys must occur when beginning in the secondarypositions of abduction, elevation, or depression, and movinginto tertiary positions. In cats, the most powerful and fatigue-resistant motor units of the LR muscle, comprising of 27% of allunits, consist of single neurons innervating fibers in both theorbital and global layers.19 These bilayer motor units wouldcommand similar contraction in the two layers, an arrange-ment convenient to maintain the position of the pulley relativeto the EOM insertion in secondary gaze positions as requiredfor the half-angle rule.

Indirect support for the functional role of the orbital layerin pulley repositioning is provided by the LPS muscle, theelevator of the eyelid. The LPS makes a path inflection fromhorizontal to nearly vertical near the location of the SR pulleyand can therefore be considered to act through a pulley.However, that there is no kinematic necessity for precise

FIGURE 10. Superior view of diagrammatic orbit showing the shifts inhorizontal rectus pulley position required to maintain the Listing’shalf-angle relationship in the tertiary positions of adducted elevationand adducted depression. Pulleys are depicted as dark rings. Paths ofthe global layers of each EOM are shown in black, whereas the orbitallayers inserting in the pulleys twice are shown in gray. The suspensionof the horizontal rectus pulleys, consisting of SM, collagen, and elastin,originates from the anterior orbital bones and is also shown in gray.

FIGURE 9. Effect of pulleys on the rotational axis of horizontal rectusEOMs. The orbit is viewed from a horizontal perspective. The rota-tional axis for any EOM is perpendicular to the line connecting thepulley to the scleral insertion and so is vertical in straight-ahead gaze(top). During saccades and pursuit eye movements with the eye in thesecondary position of elevation of (small) angle a (middle), the dis-tance D1 from the pulley (dark ring) to the globe center is equal todistance D2 from the insertion to the globe center. Thus, the rotationalaxis of the EOM tilts posteriorly by approximately angle a/2. Thissatisfies the half-angle rule to implement Listing’s law. The half-Listing’squarter-angle rule can be satisfied during the VOR (lower) if preferen-tial contraction of global layer fibers posteriorly displace the pulley sothat D1 5 3D2.


control of the LPS inflection point is consistent with the ab-sence of an orbital layer in the LPS.

The plausibility of the postulated anteroposterior pulleyshifts is supported by MRI images of EOM paths in Figure 1B.Note the similarity of the horizontal rectus paths to the diagramin Figure 10 and the appropriate direction of the shifts in pulleystructures denoted with the arrowheads, suggesting that dis-tances D1 and D2 may actually be roughly equal in livingsubjects. Note that the inflections observed in axial images ofthe horizontal rectus EOMs in the secondary positions of ab-duction and adduction may not exactly reflect the points ofinflection out of the axial plane in tertiary gaze positions. Aquantitative test of the hypothesis illustrated in Figure 10would require precise measurements of rectus EOM paths in3-D. However, the qualitative aspects of EOM path evidentfrom these images are consistent with this hypothesis. Theorbital layer insertion of each EOM on its corresponding pulleyseems ideally suited to implement the necessary pulley repo-sitioning against its elastic and SM suspensions that would, onrelaxation of orbital layer fibers, move the pulley forward. Forvisually guided or volitional eye movements conforming toListing’s law around primary gaze, global layer fibers would beexpected to receive motor commands at roughly the same gainas orbital layer fibers, to maintain the required relationshipbetween the pulley and the scleral insertion.

It has been observed experimentally that Listing’s planesfor the two eyes rotate temporally during convergence, corre-sponding to the relative excyclotorsion in depression and in-cyclotorsion in elevation41-43 necessary to maintain alignmentof corresponding retinal meridians during near viewing. Thus,during the binocular viewing of near and far targets aligned onone eye, Listing’s plane for that unmoving eye nevertheless tiltsin association with the vergence movement of the other eye.43

This tilting of Listing’s plane has been interpreted as confirma-tion of the neural nature of Listing’s law but could alternativelybe attributed to a symmetrical reconfiguration of rectus pulleysduring vergence as illustrated in Figure 11. Suitable reconfigu-ration of pulleys could include a nasal displacement of thevertical rectus pulleys due to contraction of the peribulbar SMand due to tension from posterior displacement of the MRpulley by its orbital layer transmitted to the vertical rectuspulleys through fibroelastic intercouplings. The resultant nasaldisplacement of the vertical rectus pulleys gives the verticalrectus EOMs an extorting action in depression and an intortingaction in elevation (Fig. 11), corresponding to temporal tiltingof Listing’s plane in each eye. It has been proposed by van Rijnand van den Berg41 that a form of Hering’s law of equalinnervation exists for the vergence system, such that both eyesreceive symmetric version commands for remote targets, andmirror symmetric vergence commands for near targets. Weextend this suggestion to propose that symmetric control maybe applied to the pulleys through the orbital layer rectus fibersand peribulbar SM, so that pulleys in both orbits are configuredwith mirror symmetry during convergence, regardless of su-perimposed conjugate gaze. Such a configuration could ex-plain the otherwise perplexing finding in monkeys of mirrorunits in the abducens40,44 and oculomotor nuclei.40 In thesemonkeys fixating near and far targets aligned with one eye,identified motoneurons specifically projecting to striated EOMsof the aligned (and nonmoving) eye apparently fired in re-sponse to the monocular position of the opposite eye.42 Thisotherwise astonishing finding could be reconciled if the re-

corded motoneurons projected to the orbital layer of thealigned eye and were reconfiguring the pulleys of the involvedEOMs as vergence changed.

None of the described arguments prohibits the brain fromdelivering commands to the EOMs to violate Listing’s law.15 Asproposed, the pulley system may well be specifically config-ured to violate Listing’s law during the VOR, and neural com-mands to the oblique EOMs, during the VOR or during sleep,could directly violate Listing’s law as well. However, if nocontrary neural command were given, eye movement com-mands could be specified in two dimensions, because single-unit recordings indicate they are in most premotor structures35

and the pulley system would mechanically execute 3-D eyemovements conforming to Listing’s law.15 The pulleys wouldrender horizontal and vertical eye position commands essen-tially commutative in the mathematical sense, simplifying cen-tral neural control.15,45 Any behavior of the oculomotor systemthat is noncommutative, such as maintenance of gaze stability

FIGURE 11. Superior view of diagrammatic representation of putativemechanical basis for temporal tilting of Listing’s plane during conver-gence, perhaps implemented by nasal displacement of the verticalrectus pulleys. Pulleys are depicted as dark rings. The axis of rotationof the vertical rectus EOM is shown by gray arrows for conjugateadduction (top) and convergence (bottom). Note that the rotationalaxis of the vertical rectus EOM tilts temporally in convergence com-pared with conjugate adduction, when the vertical rectus pulley isdisplaced nasally. The peribulbar SM, known to have a morphologyconsistent with implementing this nasal displacement of the verticalrectus pulleys in convergence, is shown in gray.


in darkness during various sequences of head rotations, wouldrequire explicit specification in the brain.46

Implications of the Active-Pulley Hypothesis forOcular Dynamics

The active-pulley hypothesis has major implications for oculardynamics. Raphan45 and Quaia and Optican15 have argued thatby implementing a linear plant, pulleys would effectively per-mit motor commands to the global layer to consist of the rateof change of desired eye orientation and its simple mathemat-ical integral. The pulley system would thus function as ananalog computer to convert rate of change in desired eyeorientation into the kinematically required 3-D eye velocity andwould make eye position commands essentially commutative.This simplifies the otherwise complex problem of matchingthe pulse to the step of saccadic innervation.15

Electromyographic (EMG) recordings in the human LRglobal layer demonstrate both a phasic pulse and tonic step ofactivity during saccades, the former necessary to drive theformidable viscous load imposed by the relaxing antagonistEOM and the latter necessary to oppose the lesser elastic loadas position is maintained.47 Recordings of tension at the inser-tions of simian horizontal rectus EOMs confirm the presence ofboth saccadic pulses and steps.48 In the human orbital layer,however, EMG shows only a step of activity during saccades,whereas the global layer exhibits both pulses and steps.47

Orbital layer fibers have lower recruitment thresholds thanglobal layer fibers,20,47,49 prompting Collins47 to propose thatthe orbital layer may have a special role in fixation. The insightthat the orbital layer inserts on the pulley permits an alternativeinterpretation. The mechanical load on the orbital layer is likelyto be dominated by elasticity of the attached pulley suspen-sion. Collins has pointed out that the main load on an EOMattached to the globe is viscosity arising from the relaxingantagonist EOM. A phasic pulse of force in the orbital layer isunnecessary to achieve brisk pulley motion against a mainlyelastic load. However, this elastic loading by passive connec-tive tissue requires that orbital layer fibers maintain activetension throughout the oculomotor range to avoid slack. Incontrast, global layer fibers remain under tension, even whenrelaxed, because of stretching by the antagonist EOM. Theactive-pulley hypothesis predicts that motor neurons preferen-tially innervating fibers in the orbital layer should, during sac-cades, exhibit step but not pulse changes in activity. Manysuch tonic motor neurons have been found in the abducensand oculomotor nuclei.40

Implications for Muscle Fiber Types

The active-pulley hypothesis may partially account for thecomplex variety of fiber types in EOMs, starting from thepremise that fiber characteristics are adapted to their physio-logic demands.50 Approximately 80% of fibers in the orbitallayer of each EOM are fast-twitch–generating SIFs resemblingmammalian skeletal muscle fibers, whereas 20% are MIFs thateither do not conduct action potentials or do so only in theircentral portions.16 Orbital SIFs are specialized for intense oxi-dative metabolism and fatigue resistance.16 The vascular sup-ply in the orbital layer is high,21 approximately 50% greater inhumans than the well-perfused global layer.51 The high metab-olism, fatigue resistance, and luxurious blood supply of thenumerous orbital SIFs are tailored to their continuous elastic

loading by the pulley suspensions. The expression of uniquemyosin isoforms in orbital SIFs may also be related to therequirements of fast-twitch capability against continuous load-ing, because alterations in EOM activity patterns can changeEOM-specific myosin heavy chain gene expression.52 How-ever, the function of the relatively sparse and primitive orbitalMIFs remains unclear.

Approximately 90% of fibers in the global layer are fast-twitch–generating SIFs, whereas 10% are slow, non-twitchMIFs resembling those of amphibians.16 The SIFs are oftendivided into three types—red, intermediate, and white—dis-tinguished by their density of mitochondria and fatigue resis-tance.16 The largest and most granular red SIFs, constitutingapproximately 33% of all global fibers, are very similar toorbital SIFs and are highly fatigue resistant, whereas the inter-mediate and white SIFs have progressively lower fatigue resis-tance.16 The predominant static loading of the global layer bythe moderate contractile force of antagonist EOM accounts forthe global layer’s higher overall recruitment threshold than theorbital layer and the lesser oxidative, vascular, and fatigue-resistant features of orbital SIFs. However, during saccades thehigh viscous loading of the global layer by the relaxing antag-onist EOM requires the high transient force that intermediateand white SIFs are well suited to provide. The function of thesmall number of global MIFs remains obscure.

Implications for Strabismus

Orbital SIFs are the last EOM fiber type to mature to adultfeatures and do so after birth during the establishment ofbinocular alignment.17,53 Nemestrina monkeys, a macaque spe-cies with a high prevalence of naturally occurring strabismus,show evidence of a role of orbital layer abnormalities in thepathogenesis of strabismus. These monkeys transiently exhibittubular aggregates only in orbital SIFs during the first 6 monthsof life, whereas fascicularis monkeys exhibit neither the tubu-lar aggregates in the orbital layer nor naturally occurring stra-bismus.17

Treatment of strabismus probably affects the action oforbital EOM layers on their pulleys. Botulinum toxin treatmentof strabismus produces its most lasting effects on orbital SIFs21

and may therefore alter pulley behavior. Strabismus surgerythat alters the relationships between EOM insertions and pul-leys probably produces unintended effects that should be bet-ter understood and perhaps considered in surgical planning. Inparticular, any pulley manipulation compromising the orderlyrelationship between eye orientation and the rotational axes ofEOMs would compromise neural control of eye movement15

and would be expected to produce at least dynamic binocularmisalignments in tertiary gaze positions. Noncommutativity ofocular rotations could also occur in patients who have strabis-mus with pulley abnormalities.

Acknowledgments

The authors thank Joel M. Miller and Douglas Tweed for helpfulsuggestions; James Lynch for generously providing an anatomic spec-imen; and Nicolasa De Salles, Frank Henriquez, and Zita Jian fortechnical assistance.

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